A119663 -id:A119663 - cp's OEIS frontend

A121479 Triangular numbers with more than three distinct prime factors.

210, 630, 780, 990, 1326, 1540, 1596, 1770, 1830, 2145, 2346, 2415, 2850, 2926, 3003, 3486, 3570, 3828, 4095, 4186, 4278, 4560, 4950, 5460, 5565, 6105, 6216, 6555, 6670, 6786, 7140, 7260, 7626, 8385, 8646, 8778, 9180, 9730, 9870, 10296, 10440, 10878

Offset: 1

Klaus Brockhaus, Aug 01 2006

			20*21/2 = 2*3*5*7 = 210 is the smalles triangular number with more than three distinct prime factors, hence a(1) = 210.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A000217, A068443, A119663, A121478.

Select[Accumulate[Range[200]],PrimeNu[#]>3&] (* Harvey P. Dale, Jun 06 2013 *)

for(n=1,100,k=binomial(n+1,2);if(omega(k)>3,print1(k,",")))

A121478 Triangular numbers with three distinct prime factors.

Original entry on oeis.org

66, 78, 105, 120, 190, 231, 276, 300, 378, 406, 435, 465, 528, 561, 595, 666, 741, 820, 861, 903, 946, 1035, 1128, 1176, 1275, 1378, 1485, 1653, 1953, 2016, 2080, 2211, 2278, 2485, 2556, 2628, 2775, 3081, 3160, 3240, 3655, 3741, 3916, 4005, 4371, 4465

Offset: 1

Klaus Brockhaus, Aug 01 2006

			11*12/2 = 2*3*11 = 66 is the smalles triangular number with three distinct prime factors, hence a(1) = 66.

Cf. A000217, A068443, A119663, A121479.

Select[Accumulate[Range[0, 100]] ,PrimeNu[#]==3&] (* James C. McMahon, Oct 19 2024 *)

for(n=1,100,k=binomial(n+1,2);if(omega(k)==3,print1(k,",")))

A380101 Numbers k such that omega(k-th triangular number) = 2, where omega = A001221.

Original entry on oeis.org

3, 4, 5, 6, 7, 8, 9, 10, 13, 16, 17, 18, 22, 25, 26, 31, 37, 46, 49, 53, 58, 61, 73, 81, 82, 97, 106, 121, 127, 157, 162, 166, 178, 193, 226, 241, 242, 250, 256, 262, 277, 313, 337, 346, 358, 361, 382, 397, 421, 457, 466, 478, 486, 502, 541, 562, 577, 586, 613

Offset: 1

Juri-Stepan Gerasimov, Jan 12 2025

nonn

Robert Israel, Table of n, a(n) for n = 1..10000

Supersequence of A077065 and of A178490.

Cf. A000217, A001221, A119663.

[k: k in [1..400] | #PrimeDivisors(k*(k+1) div 2) eq 2];

filter:= proc(n) local W1, n1, W2; uses numtheory;
     if n::odd then nops(factorset(n)) = 1 and nops(factorset((n+1)/2)) = 1
     else nops(factorset(n/2)) = 1 and nops(factorset(n+1)) = 1
     fi
end proc:
select(filter, [$1..1000]); # Robert Israel, Mar 12 2025

Select[Range[600], PrimeNu[#*(#+1)/2] == 2 &] (* Amiram Eldar, Jan 12 2025 *)

isok(k) = omega(k*(k+1)/2) == 2; \\ Michel Marcus, Jan 14 2025

cp's OEIS Frontend

A121479 Triangular numbers with more than three distinct prime factors.

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A121478 Triangular numbers with three distinct prime factors.

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PARI

A380101 Numbers k such that omega(k-th triangular number) = 2, where omega = A001221.

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Magma

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Mathematica

PARI